95 citations · 606 across the 55 of their papers we have counts for
69 papers
Mumford--Morita--Miller classes in generalised cohomology theories
Oscar Randal-Williams
The Mumford--Morita--Miller classes on the moduli space of Riemann surfaces may be defined not only in ordinary cohomology but in any complex-oriented cohomology theory. We begin t…
TQFTs do not detect the Milnor sphere
Ben Gripaios, Oscar Randal-Williams
We show that, under very general hypotheses, topological quantum field theories (TQFTs) cannot detect homotopy spheres bounding parallelisable manifolds, such as Milnor's exotic 7-…
Even Temperley-Lieb algebras and the dga of planar loops
Rachael Boyd, Guy Boyde, Oscar Randal-Williams +1
We show that the homology of a Temperley-Lieb algebra on an even number of strands has a rich algebraic structure and is highly nontrivial in general. This is achieved by proving t…
A chromatic approach to homological stability
Oscar Randal-Williams
We propose a way to organise the subject of ``higher-order homological stability'', in the context of a graded -algebra , along the same lines that the chromatic p…
Smoothing topological pseudo-isotopies of 4-manifolds
Patrick Orson, Mark Powell, Oscar Randal-Williams
Given a closed, smooth 4-manifold and self-diffeomorphism that is topologically pseudo-isotopic to the identity, we study the question of whether is moreover smoothly p…
Homological stability for general linear groups over Dedekind domains
Oscar Randal-Williams
We prove a new kind of homological stability theorem for automorphism groups of finitely-generated projective modules over Dedekind domains, which takes into account all possible s…
Uniform twisted homological stability
Jeremy Miller, Peter Patzt, Dan Petersen +1
We prove a homological stability theorem for families of discrete groups (e.g. mapping class groups, automorphism groups of free groups, braid groups) with coefficients in a sequen…
Smooth generalized symmetries of quantum field theories
Ben Gripaios, Oscar Randal-Williams, Joseph Tooby-Smith
Dynamical quantum field theories (QFTs), such as those in which spacetimes are equipped with a metric and/or a field in the form of a smooth map to a target manifold, can be formul…
The Alexander trick for homology spheres
Soren Galatius, Oscar Randal-Williams
We show that the group of homeomorphisms of a compact contractible -manifold which fix the boundary is contractible, as long as . We deduce this from a strong uniquene…
Monodromy and mapping class groups of 3-dimensional hypersurfaces
Oscar Randal-Williams
We describe the subgroup of the mapping class group of a hypersurface in consisting of those diffeomorphisms which can be realised by monodromy.
Configuration spaces as commutative monoids
Oscar Randal-Williams
After 1-point compactification, the collection of all unordered configuration spaces of a manifold admits a commutative multiplication by superposition of configurations. We explai…
On the cohomology of Torelli groups. II
Oscar Randal-Williams
We describe the ring structure of the rational cohomology of the Torelli groups of the manifolds in a stable range, for . Some of our results are a…
Generalized symmetries of topological field theories
Ben Gripaios, Oscar Randal-Williams, Joseph Tooby-Smith
We study generalized symmetries in a simplified arena in which the usual quantum field theories of physics are replaced with topological field theories and the smooth structure wit…
Algebraic independence of topological Pontryagin classes
Soren Galatius, Oscar Randal-Williams
We show that the topological Pontryagin classes are algebraically independent in the rationalised cohomology of BTop(d) for all .
Classical homological stability from the point of view of cells
Oscar Randal-Williams
We explain how to interpret the complexes arising in the "classical" homology stability argument (e.g. in the framework of Randal-Williams--Wahl) in terms of higher algebra, which…
The family signature theorem
Oscar Randal-Williams
We discuss several versions of the Family Signature Theorem: in rational cohomology using ideas of Meyer, in -theory using ideas of Sullivan, and finally in symme…
Stable cohomology of congruence subgroups
Oscar Randal-Williams
We describe the -cohomology of the congruence subgroups in degrees , for all large enough , establishing a formula proposed by F.…
Diffeomorphisms of discs
Oscar Randal-Williams
I describe what is currently known, for , about the rational homotopy type of the group of diffeomorphisms of the -disc relative to its boundary, and the closely relat…
Diffeomorphisms of discs and the second Weiss derivative of BTop(-)
Manuel Krannich, Oscar Randal-Williams
We compute the rational homotopy groups in degrees up to approximately d of the group of diffeomorphisms of a closed d-dimensional disc fixing the boundary. Based on…
On the Torelli Lie algebra
Alexander Kupers, Oscar Randal-Williams
We prove two theorems about the Malcev Lie algebra associated to the Torelli group of a surface of genus : stably, it is Koszul and the kernel of the Johnson homomorphism consis…
Mapping class groups of simply connected high-dimensional manifolds need not be arithmetic
Manuel Krannich, Oscar Randal-Williams
It is well known that Sullivan showed that the mapping class group of a simply connected high-dimensional manifold is commensurable with an arithmetic group, but the meaning of "co…
On the order of Dehn twists
Ailsa Keating, Oscar Randal-Williams
This note records the order of a higher dimensional Dehn twist in a range of topologically significant groups.
Differential cohomology and topological actions in physics
Joe Davighi, Ben Gripaios, Oscar Randal-Williams
We use differential cohomology to systematically construct a large class of topological actions in physics, including Chern-Simons terms, Wess-Zumino-Novikov-Witten terms, and thet…
On automorphisms of high-dimensional solid tori
Mauricio Bustamante, Oscar Randal-Williams
We study the infinite generation in the homotopy groups of the group of diffeomorphisms of , for , in a range of degrees up to . Our analysis r…